Cyclostationary Phase Conditioning for Medical Time Series Diffusion

Samuel Ruiperez-Campillo; Michele Copetti; Jorge da Silva Goncalves; Sonia Laguna; Thomas Hofmann; Julia E. Vogt

cs.LGSep 28, 2026

Cyclostationary Phase Conditioning for Medical Time Series Diffusion

Authors: Samuel Ruiperez-Campillo, Michele Copetti, Jorge da Silva Goncalves, Sonia Laguna, Thomas Hofmann, Julia E. Vogt

Organizations: Dept. of Computer Science ETH Zurich

Abstract

Many physiological time series, such as cardiac and brain recordings, exhibit cyclostationarity: their statistics vary periodically with an underlying cycle phase. Corruption from motion, poor contact, and physiological interference obscures morphology needed for diagnosis, making signal restoration essential. Existing diffusion approaches condition on corrupted observations alone and must learn cyclic structure implicitly. We instead propose two inductive biases which encode cyclostationarity: a shift-covariant wavelet representation and dense per-sample phase conditioning inferred from the corrupted input. We further introduce a training-free cyclostationarity index that quantifies phase structure and predicts when phase conditioning will help. Finally, we propose antithetic coupling of reverse trajectories to reduce sampling variance while achieving comparable performance with fivefold fewer network evaluations. Across modalities, our results show that explicitly encoding measurable cyclic structure improves physiological time-series restoration.

Figures & tables

Figure 1: Overview of PTSDiff . The corrupted observation

y

feeds the context encoder and the phase encoder; it is frame-transformed (top) and concatenated with the frame-transformed phase channels (middle) and the latent

x_{t}^{\mathrm{F}}

as U-Net input. The context encoder (bottom) modulates the backbone through FiLM embeddings, and the U-Net drives the update to

x_{t-1}^{\mathrm{F}}

. Block-level detail is in Figure .

	Task	Baseline	PTSDiff
PPG	HR MAE $\downarrow$	5.947	5.155
ECG	PTB-XL AUROC $\uparrow$	0.840	0.848
ECG	MIT-BIH F1 $\uparrow$	0.543	0.630
EMG	Activation bal. acc. $\uparrow$	0.749	0.750
EEG	Band-power error $\downarrow$	4.56	3.31

Table 2: Downstream utility across modalities. Extended results in Table .

Figure 3: Synthetic sweep:

\Delta

SNR gain over the no-periodicity ablation versus the cyclostationarity index

\Pi

. Further details in Appendix .

Frame			Analytical	Auxiliary
(SWT)	Phase	Context	phase	loss	$\Delta$ SNR $\uparrow$	PRD [%] $\downarrow$	CC $\uparrow$
$\checkmark$	–	–	–	$\checkmark$	$15.05\pm 0.21$	$25.51\pm 0.60$	$0.96\pm 0.00$
$\checkmark$	–	$\checkmark$	–	$\checkmark$	$15.36\pm 0.21$	$24.54\pm 0.55$	$0.96\pm 0.00$
$\checkmark$	$\checkmark$	–	–	$\checkmark$	$15.28\pm 0.20$	$25.35\pm 0.65$	$0.96\pm 0.00$
$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	$15.34\pm 0.21$	$24.50\pm 0.54$	$0.96\pm 0.00$
$\checkmark$	$\checkmark$	$\checkmark$	–	–	$15.52\pm 0.21$	$24.01\pm 0.53$	$0.96\pm 0.00$

Table 3: Component ablation on ECG (PTB-XL, SNR

-2.0

dB, one antithetic pair, single seed; mean

\pm

95% CI). Phase from a classical detector performs similarly to no phase; the learned encoder improves on both.

Figure 4: Sampling efficiency on ECG. A single antithetic pair (AV-2) outperforms ten independent trajectories (MC-10) with

5\times

fewer NFEs. Wall-clock time decreases similarly. Extended results in Figure .

Appendix figures & tables30 assets

Supplementary material from the paper’s appendix.

Appendix

Modality	Detector mode	Refractory [ms]	Smoothing [ms]	Event width [ms]	Threshold scale	$f_{\min}$ [Hz]	$f_{\max}$ [Hz]
ECG	QRS peaks	$220$	$80$	$35$	$0.5$	$0.5$	$3.0$

Appendix

Table 4: Analytical ECG cycle-event detector used to construct the warm-start target

\Phi^{\star}=\mathcal{D}(x_{0})

. Its parameters are fixed and the detector is not used at inference.

Hyperparameter	ECG	PPG	EEG	EMG
Learning rate	$1\times 10^{-4}$	$1\times 10^{-3}$	$5\times 10^{-4}$	$1\times 10^{-4}$
Scheduler	MultiStepLR	ReduceLROnPlateau	MultiStepLR	ReduceLROnPlateau
Scheduler settings	milestones $(0.4,0.7,0.9)$ , $\gamma=0.1$	factor $0.5$ , patience $10$	milestones $(0.95)$ , $\gamma=0.1$	factor $0.5$ , patience $5$
Phase warm-start	Yes	No	No	No
Wavelet	Sym4	Sym4	Db4	Sym4
Decomposition levels $J$	4	4	4	4

Appendix

Table 5: Training hyperparameters across modalities. Frame, backbone, diffusion schedule, objective form and sampler are shared; only the specified entries differ. EEG uses a different wavelet and morphology weight inherited from an earlier configuration that continues to perform better for that modality; a full ablation matching Tables and has not been run for EEG.

Figure 5: Block-level architecture of PTSDiff , complementing the overview in Figure . (a) Phase encoder

\mathcal{E}_{ph}

: a convolutional stem, six dilated residual blocks (

d=1,2,4,8,16,32

) whose receptive field spans several cycles, and a projection to the five channels of the predicted phase field

\hat{\Phi}

, which is then frame-transformed as

\hat{\Phi}^{\mathrm{F}}=\mathcal{W}(\hat{\Phi})

. (b) Context encoder

\mathcal{E}_{ctx}

: three strided stages followed by global average pooling, emitting one pooled embedding

c_{y}^{(\ell)}

per U-Net resolution and a global embedding

c_{y}^{(g)}

. (c) SWT-domain denoising U-Net

\epsilon_{\theta}

, taking the channel-wise concatenation

x_{t}^{\mathrm{F}}\,\|\,y^{\mathrm{F}}\,\|\,\hat{\Phi}^{\mathrm{F}}

(

7(J{+}1)=35

channels at

J=4

) and predicting

\hat{\epsilon}_{t}

; dashed arrows are skip connections. (d–f) Internal structure of the Conv-Block, the FiLM-modulated ResBlock and the dilated residual block. Each detail panel carries the colour of the block it expands, and the letter shown at a block type’s first occurrence points to its panel.

\times k

denotes

k

stacked blocks. Decoder FiLM connections and the diffusion-step embedding are omitted for clarity.

Setting	Metric	Direction	Definition
All modalities	$\Delta$ SNR	$\uparrow$	$\mathrm{SNR}(x_{0},\hat{x}_{0})-\mathrm{SNR}(x_{0},y)$
All modalities	PRD	$\downarrow$	$100\sqrt{\sum_{n}e[n]^{2}/\sum_{n}(x_{0}[n]-\bar{x}_{0})^{2}}$
All modalities	CC	$\uparrow$	$\frac{\sum_{n}(x_{0}[n]-\bar{x}_{0})(\hat{x}_{0}[n]-\bar{\hat{x}}_{0})}{\sqrt{\sum_{n}(x_{0}[n]-\bar{x}_{0})^{2}\sum_{n}(\hat{x}_{0}[n]-\bar{\hat{x}}_{0})^{2}}}$
ECG	SSD	$\downarrow$	$\sum_{n}e[n]^{2}$
ECG	MAD	$\downarrow$	$\max_{n}\|e[n]\|$
ECG	CosSim	$\uparrow$	$\langle x_{0},\hat{x}_{0}\rangle/(\\|x_{0}\\|_{2}\\|\hat{x}_{0}\\|_{2})$

Appendix

Table 6: Evaluation metrics. The first block is reported for every modality; the remainder are the benchmark-specific metrics conventionally used in each literature.

Dataset	Model	$\Delta$ SNR $\uparrow$	PRD [%] $\downarrow$	CC $\uparrow$	SSD $\downarrow$	MAD $\downarrow$	CosSim $\uparrow$
PTB-XL	Noisy ( $\mathrm{SNR}_{\mathrm{in}}=-2.0$ dB)	$0.00$	$152.86\pm 3.67$	$0.61\pm 0.01$	$210.66\pm 17.44$	$0.60\pm 0.02$	$0.60\pm 0.01$
	FIR filter	$7.44\pm 0.14$	$64.13\pm 1.44$	$0.83\pm 0.01$	$35.52\pm 2.61$	$0.36\pm 0.01$	$0.83\pm 0.01$
	SWT denoising	$6.22\pm 0.16$	$68.16\pm 1.19$	$0.76\pm 0.01$	$35.02\pm 2.16$	$0.35\pm 0.01$	$0.76\pm 0.01$
	TCDAE	$12.29\pm 0.17$	$34.03\pm 0.65$	$0.95\pm 0.00$	$8.71\pm 0.76$	$0.25\pm 0.01$	$0.95\pm 0.00$
	DeScoD-1	$11.82\pm 0.19$	$36.11\pm 0.70$	$0.92\pm 0.00$	$10.14\pm 0.97$	$0.26\pm 0.01$	$0.92\pm 0.00$
	DeScoD-3	$13.18\pm 0.19$	$31.04\pm 0.61$	$0.94\pm 0.00$	$7.73\pm 0.89$	$0.22\pm 0.01$	$0.94\pm 0.00$

Appendix

Table 7: Denoising comparison across ECG datasets (PTB-XL, QTDB, MIT-BIH). Values are mean

\pm

95% CI.

\uparrow

higher is better,

\downarrow

lower is better. Bold and underlined values mark the best and second-best denoising method within each dataset and metric.

Noise level	Model	$\Delta$ SNR $\uparrow$	PRD [%] $\downarrow$	CC $\uparrow$	SSD $\downarrow$	MAD $\downarrow$	CosSim $\uparrow$
0.2-0.6	Noisy	$0.00$	$55.45\pm 2.05$	$0.87\pm 0.01$	$22.48\pm 2.70$	$0.21\pm 0.01$	$0.87\pm 0.01$
	FIR filter	$6.79\pm 0.28$	$25.28\pm 0.92$	$0.96\pm 0.00$	$4.68\pm 0.63$	$0.13\pm 0.01$	$0.96\pm 0.00$
	SWT denoising	$3.04\pm 0.38$	$38.20\pm 1.12$	$0.92\pm 0.01$	$9.88\pm 1.57$	$0.17\pm 0.01$	$0.92\pm 0.01$
	TCDAE	$8.14\pm 0.34$	$21.25\pm 0.67$	$0.98\pm 0.00$	$2.66\pm 0.32$	$0.13\pm 0.01$	$0.98\pm 0.00$
	DeScoD-1	$7.49\pm 0.35$	$23.23\pm 0.88$	$0.97\pm 0.00$	$3.73\pm 0.60$	$0.12\pm 0.01$	$0.97\pm 0.00$
	DeScoD-3	$8.83\pm 0.37$	$20.08\pm 0.80$	$0.98\pm 0.00$	$3.00\pm 0.59$	$0.11\pm 0.01$	$0.98\pm 0.00$

Appendix

Table 8: Denoising comparison by noise level on PTB-XL. Values are mean

\pm

95% CI.

\uparrow

higher is better,

\downarrow

lower is better. Bold marks the best and underline the second best within each bin and metric.

Noise level	Model	$\Delta$ SNR $\uparrow$	PRD [%] $\downarrow$	CC $\uparrow$	SSD $\downarrow$	MAD $\downarrow$	CosSim $\uparrow$
0.2-0.6	Noisy	$0.00$	$48.26\pm 0.49$	$0.90\pm 0.00$	$48.54\pm 2.29$	$0.29\pm 0.00$	$0.90\pm 0.00$
	FIR filter	$4.52\pm 0.09$	$27.97\pm 0.26$	$0.96\pm 0.00$	$15.92\pm 0.79$	$0.27\pm 0.01$	$0.96\pm 0.00$
	SWT denoising	$3.05\pm 0.10$	$32.84\pm 0.27$	$0.95\pm 0.00$	$23.19\pm 1.52$	$0.24\pm 0.00$	$0.94\pm 0.00$
	TCDAE	$5.02\pm 0.10$	$26.09\pm 0.21$	$0.98\pm 0.00$	$16.57\pm 1.51$	$0.28\pm 0.01$	$0.97\pm 0.00$
	DeScoD-10	$6.08\pm 0.11$	$23.66\pm 0.24$	$0.97\pm 0.00$	$24.91\pm 4.52$	$0.24\pm 0.01$	$0.97\pm 0.00$
	TFCDiff-10	$6.81\pm 0.11$	$22.32\pm 0.27$	$0.98\pm 0.00$	$32.81\pm 6.16$	$0.21\pm 0.01$	$0.97\pm 0.00$

Appendix

Table 9: Denoising comparison by noise level on QTDB. Values are mean

\pm

95% CI.

\uparrow

higher is better,

\downarrow

lower is better. Bold marks the best and underline the second best within each bin and metric.

Noise level	Model	$\Delta$ SNR $\uparrow$	PRD [%] $\downarrow$	CC $\uparrow$	SSD $\downarrow$	MAD $\downarrow$	CosSim $\uparrow$
0.2-0.6	Noisy	$0.00$	$52.72\pm 1.51$	$0.88\pm 0.00$	$98.31\pm 9.28$	$0.44\pm 0.02$	$0.88\pm 0.01$
	FIR filter	$5.15\pm 0.26$	$28.56\pm 0.79$	$0.96\pm 0.00$	$27.96\pm 2.82$	$0.37\pm 0.02$	$0.96\pm 0.00$
	SWT denoising	$3.28\pm 0.29$	$34.95\pm 0.86$	$0.93\pm 0.00$	$49.65\pm 6.14$	$0.36\pm 0.02$	$0.93\pm 0.00$
	TCDAE	$6.63\pm 0.29$	$23.87\pm 0.60$	$0.97\pm 0.00$	$22.28\pm 3.97$	$0.41\pm 0.02$	$0.97\pm 0.00$
	DeScoD-10	$6.58\pm 0.31$	$24.96\pm 0.77$	$0.96\pm 0.00$	$26.46\pm 3.73$	$0.38\pm 0.02$	$0.96\pm 0.00$
	TFCDiff-10	$6.27\pm 0.33$	$26.59\pm 0.91$	$0.96\pm 0.00$	$40.82\pm 6.68$	$0.39\pm 0.03$	$0.96\pm 0.00$

Appendix

Table 10: Denoising comparison by noise level on MIT-BIH. Values are mean

\pm

95% CI.

\uparrow

higher is better,

\downarrow

lower is better. Bold marks the best and underline the second best within each bin and metric.

Figure 6: Restoration across corruption levels for PPG-DaLiA (a), NinaPro (b) and EEGdenoiseNet (c), grouped by each modality’s corruption grid. The $y$ -intercept marks the average per model and metric; arrows indicate the better direction.

Figure 7: Restoration across corruption levels using each benchmark’s own metrics. (a) PPG-DaLiA ( $\Delta$ SNR, RMSE, PRD), following Lai et al. (2025) . (b) NinaPro ( $\Delta$ SNR, RMSE, ARV, MF), following Liu et al. (2024) . (c) EEGdenoiseNet ( $\Delta$ SNR, CC, temporal and spectral RRMSE), following Huang et al. (2025) . On PPG and EEG the ordering follows the main metrics; on EMG, ARV and mean-frequency error are more mixed under heavy corruption, consistent with trajectory averaging mildly smoothing amplitude and spectral summaries (Appendix ).

Figure 8: ECG Cross-dataset generalization to MIT-BIH (a) and QTDB (b) without retraining. Error bars are 95% CI.

Modality	Train	Held-out	Best baseline	$\Delta$ SNR $\uparrow$	$\Delta$	PRD [%] $\downarrow$	$\Delta$	CC $\uparrow$	$\Delta$
PPG	PPG-DaLiA	BIDMC	DDAE	$16.41$	$+2.08$	$32.06$	$+8.09$	$0.945$	$+0.048$
ECG	PTB-XL	MIT-BIH	DeScoD-10	$13.88$	$+2.63$	$27.93$	$+9.83$	$0.949$	$+0.039$
ECG	PTB-XL	QTDB	TFCDiff-10	$13.23$	$+1.52$	$26.51$	$+5.35$	$0.963$	$+0.019$
EMG	NinaPro DB2	NinaPro DB3	SDEMG	$23.45$	$+1.49$	$16.16$	$+3.20$	$0.985$	$+0.007$
EEG	EEGdenoiseNet	EEGMMIDB	EEGIFNet	$5.35$	$-0.37$	$56.18$	$-2.75$	$0.808$	$-0.029$

Appendix

Table 11: Dataset shift for all modalities: train on one dataset, evaluate on a held-out dataset with no retraining, against the strongest restoration baseline on the held-out set (named per row).

\Delta

columns give the margin of PTSDiff -AV-10 over that baseline (positive = PTSDiff better) on each of the three main metrics.

Baseline	Metric	MIT-BIH	PTB-XL	QTDB
TFCDiff-10	$\Delta$ SNR	$+2.68^{***}$ $p_{adj}=<1e-300$	$+2.62^{***}$ $p_{adj}=<1e-300$	$+1.52^{***}$ $p_{adj}=<1e-300$
	PRD [%]	$-9.92^{***}$ $p_{adj}=<1e-300$	$-7.48^{***}$ $p_{adj}=<1e-300$	$-5.35^{***}$ $p_{adj}=<1e-300$
	CC	$+0.035^{***}$ $p_{adj}=<1e-300$	$+0.024^{***}$ $p_{adj}=3.4e-290$	$+0.019^{***}$ $p_{adj}=<1e-300$
TCDAE	$\Delta$ SNR	$+2.67^{***}$ $p_{adj}=<1e-300$	$+3.80^{***}$ $p_{adj}=<1e-300$	$+2.90^{***}$ $p_{adj}=<1e-300$
	PRD [%]	$-9.17^{***}$ $p_{adj}=<1e-300$	$-11.60^{***}$ $p_{adj}=<1e-300$	$-9.71^{***}$ $p_{adj}=<1e-300$
	CC	$+0.019^{***}$ $p_{adj}=<1e-300$	$+0.013^{***}$ $p_{adj}=1.3e-263$	$+0.018^{***}$ $p_{adj}=<1e-300$

Appendix

Table 12: Paired statistical comparison of PTSDiff -AV-10 against denoising baselines across the main metrics. Each cell reports the mean paired difference ( PTSDiff -AV-10

-

baseline) in the metric’s native units, with the Holm–Bonferroni-adjusted

p

-value below.

\Delta

SNR (dB) and CC are higher-is-better, PRD (percentage points) is lower-is-better; stars mark where PTSDiff -AV-10 is significantly better.

	Per-class AUROC					Macro
Model	CD	HYP	MI	NORM	STTC	AUROC
clean	.871 $\pm$ .019	.782 $\pm$ .031	.845 $\pm$ .020	.916 $\pm$ .012	.878 $\pm$ .017	.859 $\pm$ .011
noisy	.830 $\pm$ .022	.722 $\pm$ .034	.753 $\pm$ .024	.866 $\pm$ .015	.822 $\pm$ .020	.799 $\pm$ .012
FIR Filter	.828 $\pm$ .023	.729 $\pm$ .034	.758 $\pm$ .025	.855 $\pm$ .015	.818 $\pm$ .020	.798 $\pm$ .012
SWT Denoising	.788 $\pm$ .024	.716 $\pm$ .032	.658 $\pm$ .028	.798 $\pm$ .019	.772 $\pm$ .024	.746 $\pm$ .013
TCDAE	.855 $\pm$ .020	.760 $\pm$ .033	.829 $\pm$ .022	.902 $\pm$ .013	.853 $\pm$ .018	.840 $\pm$ .012

Appendix

Table 13: Per-superdiagnostic-class and macro-averaged AUROC on PTB-XL. Values are point estimates with 95% bootstrap confidence intervals. Bold/underlined: best/second-best (excluding clean/noisy).

Model	AUROC	Specificity	Sensitivity	F1
clean	.926 $\pm$ .004	.991 $\pm$ .001	.580 $\pm$ .014	.703 $\pm$ .012
noisy	.718 $\pm$ .008	.989 $\pm$ .001	.151 $\pm$ .010	.243 $\pm$ .014
FIR Filter	.734 $\pm$ .008	.990 $\pm$ .001	.157 $\pm$ .010	.254 $\pm$ .014
SWT Denoising	.722 $\pm$ .008	.971 $\pm$ .002	.206 $\pm$ .011	.286 $\pm$ .014
TCDAE	.839 $\pm$ .007	.979 $\pm$ .001	.436 $\pm$ .013	.543 $\pm$ .013
DeScoD	.822 $\pm$ .007	.919 $\pm$ .003	.541 $\pm$ .014	.490 $\pm$ .011

Appendix

Table 14: Downstream classification on MIT-BIH binary beat classification. Values are point estimates with 95% bootstrap confidence intervals. Bold/underlined: best/second-best (excluding clean/noisy).

Sensitivity
Class	clean	noisy	FIR Filter	SWT Denoising	TCDAE	DeScoD	TFCDiff	PTSDiff -MC-10	PTSDiff -AV-10
CD	.695 $\pm$ .041	.592 $\pm$ .043	.727 $\pm$ .040	.775 $\pm$ .035	.641 $\pm$ .043	.647 $\pm$ .041	.683 $\pm$ .041	.691 $\pm$ .039	.679 $\pm$ .041
HYP	.520 $\pm$ .066	.143 $\pm$ .046	.161 $\pm$ .050	.184 $\pm$ .053	.534 $\pm$ .066	.592 $\pm$ .067	.583 $\pm$ .064	.538 $\pm$ .065	.543 $\pm$ .065
MI	.662 $\pm$ .044	.827 $\pm$ .036	.880 $\pm$ .031	.954 $\pm$ .021	.600 $\pm$ .048	.585 $\pm$ .045	.624 $\pm$ .042	.621 $\pm$ .045	.624 $\pm$ .045
NORM	.892 $\pm$ .019	.446 $\pm$ .033	.425 $\pm$ .031	.166 $\pm$ .024	.893 $\pm$ .019	.880 $\pm$ .020	.860 $\pm$ .022	.905 $\pm$ .019	.905 $\pm$ .018
STTC	.669 $\pm$ .044	.862 $\pm$ .031	.675 $\pm$ .043	.669 $\pm$ .041	.614 $\pm$ .047	.650 $\pm$ .045	.638 $\pm$ .044	.610 $\pm$ .046	.606 $\pm$ .045

Appendix

Table 15: Per-superdiagnostic-class and macro-averaged sensitivity, specificity, and F1 on PTB-XL. Values are point estimates with 95% bootstrap confidence intervals. Bold/underlined: best/second-best per row (excluding clean/noisy).

Modality	Task (metric)	Clean	Corrupted	Best baseline	PTSDiff -AV-10
PPG	HR estimation (MAE, bpm) $\downarrow$	$4.772$	$8.483$	$5.947$	$\mathbf{5.155}$
ECG	PTB-XL superdiagnostic (macro AUROC) $\uparrow$	$.859$	$.799$	$.840$	$\mathbf{.848}$
ECG	MIT-BIH beat classification (F1) $\uparrow$	$.703$	$.243$	$.543$	$\mathbf{.630}$
EMG	NinaPro DB2 muscle activation (balanced acc.) $\uparrow$	$.755$	$.501$	$.749$	$\mathbf{.750}$
EEG	Band-power preservation ( $\alpha,\beta$ rel. error, %) $\downarrow$	$0.00$	$4.75$	$4.56$	$\mathbf{3.31}$

Appendix

Table 16: Downstream utility across all four modalities.

Ablation ( $\Delta$ from full model, dB)	PPG	ECG	EMG	EEG
$-$ Phase conditioning	$-1.82\pm 0.03$	$-0.64\pm 0.05$	$+0.05\pm 0.01$	$-0.24\pm 0.01$
$-$ Temporal context	$+0.28\pm 0.02$	$-0.72\pm 0.07$	$-0.35\pm 0.01$	$-0.27\pm 0.01$
$-$ Shift-covariant frame	$+0.37\pm 0.03$	$-0.51\pm 0.05$	$-0.51\pm 0.01$	$-0.74\pm 0.02$
$-$ Auxiliary losses	$-0.59\pm 0.02$	$-0.48\pm 0.05$	$+0.02\pm 0.01$	$-2.80\pm 0.04$
Analytical phase (vs. learned)	–	$-0.66\pm 0.05$	–	–

Appendix

Table 17: Component ablation replicated across modalities. Cells report the change in

\Delta

SNR relative to the full model on the same dataset as mean

\pm

95% bootstrap CI. The analytical phase row is reported only for ECG, where the detector comparison is part of the main mechanism analysis. Values use one antithetic-variates pair.

Modality	Dataset	AC window [Hz]	$\Pi_{\mathrm{AC}}$ [95% CI]	$\hat{\Pi}$ [95% CI]
PPG	PPG-DaLiA	0.5–3	$0.62$ [ $0.60$ , $0.63$ ]	–
	BIDMC †	0.5–3	$0.85$ [ $0.81$ , $0.89$ ]	–
	Mean		$0.74$	–
ECG	PTB-XL	0.5–3	$0.71$ [ $0.70$ , $0.72$ ]	$0.87$ [ $0.86$ , $0.87$ ]
	QTDB †	0.5–3	$0.81$ [ $0.78$ , $0.83$ ]	$0.94$ [ $0.92$ , $0.95$ ]
	MIT-BIH †	0.5–3	$0.61$ [ $0.56$ , $0.66$ ]	$0.80$ [ $0.70$ , $0.87$ ]

Appendix

Table 18: Cyclostationarity of the clean test sets, ordered by the mean

\Pi_{\mathrm{AC}}

, which is the autocorrelation proxy of Appendix , computed identically for every dataset in a per-modality lag window fixed before analysis.

\hat{\Pi}

(Definition ) requires a reliable cycle detector and is reported for ECG only (Table ). † Held-out datasets, evaluated without retraining (Table ); Mean rows average the datasets of each modality. Because the proxy takes its peak at a single lag within each window, beat-to-beat rate variability lowers it, and it reads below

\hat{\Pi}

on ECG. Brackets are 95% cluster-bootstrap CIs.

		Metric	Daubechies			Symlets			Coiflets
		Metric	db 4	db 6	db 8	sym 4	sym 6	sym 8	coif 3	coif 4	coif 5
$J$	2	$\Delta$ SNR $\uparrow$	$15.57\pm 0.21$	$15.46\pm 0.20$	$15.16\pm 0.21$	$15.13\pm 0.21$	$15.57\pm 0.21$	$15.47\pm 0.20$	$15.21\pm 0.20$	$15.39\pm 0.21$	$15.38\pm 0.21$
	2	PRD $\downarrow$	$24.21\pm 0.62$	$24.49\pm 0.58$	$25.80\pm 0.69$	$25.13\pm 0.57$	$24.01\pm 0.58$	$24.43\pm 0.60$	$24.79\pm 0.56$	$24.91\pm 0.64$	$24.54\pm 0.58$
	4	$\Delta$ SNR $\uparrow$	$15.67\pm 0.21$	$15.50\pm 0.21$	$15.35\pm 0.21$	$15.98\pm 0.21$	$15.76\pm 0.21$	$15.60\pm 0.21$	$15.49\pm 0.21$	$15.43\pm 0.21$	$15.41\pm 0.21$
	4	PRD $\downarrow$	$23.62\pm 0.56$	$24.09\pm 0.54$	$24.54\pm 0.56$	$22.73\pm 0.50$	$23.33\pm 0.52$	$24.14\pm 0.62$	$24.28\pm 0.58$	$24.33\pm 0.57$	$24.43\pm 0.56$
	6	$\Delta$ SNR $\uparrow$	$15.07\pm 0.20$	$14.86\pm 0.21$	$14.91\pm 0.21$	$15.24\pm 0.21$	$14.93\pm 0.21$	$15.07\pm 0.20$	$14.86\pm 0.20$	$14.89\pm 0.20$	$14.95\pm 0.20$

Appendix

Table 19: PTSDiff SWT ablation on PTB-XL:

\Delta

SNR (dB, higher better) and PRD (%, lower better) per (wavelet, decomposition level J), single antithetic-variate (AV) pair. Cells are mean

\pm

95% CI; best per metric in bold .

		Metric	$\lambda_{\mathrm{reconstruction}}$
		Metric	0.05	0.1	0.2	0.3	0.5	1
$\lambda_{\mathrm{morphology}}$	0.05	$\Delta$ SNR $\uparrow$	$15.61\pm 0.20$	$15.65\pm 0.21$	$15.57\pm 0.21$	$15.66\pm 0.20$	$15.74\pm 0.21$	$15.57\pm 0.21$
	0.05	PRD $\downarrow$	$23.74\pm 0.53$	$23.70\pm 0.56$	$24.16\pm 0.62$	$23.78\pm 0.57$	$23.48\pm 0.54$	$24.03\pm 0.58$
	0.1	$\Delta$ SNR $\uparrow$	$15.54\pm 0.21$	$15.57\pm 0.21$	$15.30\pm 0.21$	$15.79\pm 0.19$	$15.59\pm 0.21$	$15.00\pm 0.21$
	0.1	PRD $\downarrow$	$23.98\pm 0.55$	$23.86\pm 0.54$	$24.54\pm 0.54$	$23.29\pm 0.54$	$23.84\pm 0.54$	$25.25\pm 0.54$
	0.2	$\Delta$ SNR $\uparrow$	$15.47\pm 0.21$	$15.61\pm 0.22$	$15.60\pm 0.21$	$15.65\pm 0.21$	$15.66\pm 0.21$	$15.65\pm 0.21$

Appendix

Table 20: PTSDiff auxiliary-loss weighting ablation on PTB-XL:

\Delta

SNR (dB, higher better) and PRD (%, lower better) per (morphology, reconstruction) loss weight, single antithetic-variate (AV) pair. Cells are mean

\pm

95% CI; best per metric in bold . Ablations use the full model with a db4 wavelet and 4 decomposition levels.

Figure 9: Change in restoration performance when phase-encoder features are shuffled across samples within a batch. Values are the $\Delta$ SNR difference between correctly matched and shuffled phase fields.

Figure 10: Empirical antithetic-pair correlation. (a) Variance-weighted correlation $\widehat{\bar{\rho}}_{t}$ over the 50 post-update states $t=T-1,\ldots,0$ , with 95% confidence intervals. (b) Output correlation $\widehat{\bar{\rho}}_{0}$ : transparent points are single fixed observations, diamonds are modality aggregates with 95% confidence intervals.

Figure 11: Quality–compute frontier on ECG. PRD, CC and

\Delta

SNR against NFE, for independent (MC) and antithetically coupled (AV) sampling. The dotted line marks a single antithetic pair, which already exceeds ten independent trajectories. TCDAE is deterministic and therefore flat. Arrows indicate the better direction.

Model / sampler	NFE	Params [M]	Wall-clock [ms]	$\Delta$ SNR $\uparrow$	$\Delta$ vs. MC
DeScoD-ECG, MC-10	$500$	$1.93$	$361$	$13.78$	—
DeScoD-ECG, AV-2	$100$	$1.93$	$72$	$13.86$	$+0.08$
TFCDiff, MC-10	$500$	$4.12$	$803$	$13.47$	—
TFCDiff, AV-2	$100$	$4.12$	$161$	$13.67$	$+0.20$
PTSDiff , MC-10	$500$	$3.44$	$267$	$15.79$	—
PTSDiff , AV-2	$100$	$3.44$	$53$	$16.00$	$+0.21$

Appendix

Table 21: Antithetic coupling applied to competing diffusion restorers without retraining (sampler swap only), with matched-NFE compute accounting. Establishes whether Proposition is a property of the sampler or of PTSDiff .

Figure 12: Per-sample $\Delta$ SNR on the PTB-XL test set. Notched box plots: box is the IQR, white line the median, notch its 95% CI, whiskers span $1.5\times$ IQR, open circles are outliers. Top: overall (white diamond = mean). Bottom: stratified by corruption scaling factor $\lambda$ .

Figure 13: Four-level stationary wavelet decomposition with the sym4 wavelet: one approximation and four detail channels, all at the input length. (a) Clean signal. (b) Corrupted signal.

Figure 14: ECG under heavy corruption. Left: clean, corrupted, and reconstructions from PTSDiff -AV-10 and the strongest baselines on a representative PTB-XL test sample. Right: time–frequency representations of the clean (top), corrupted (middle) and PTSDiff -AV-10 reconstructed (bottom) signal.

Figure 15: ECG under light corruption ( $\lambda\in[0.2,0.6]$ ). (a) Clean, corrupted, and reconstructions. (b) Corresponding spectrograms.

Figure 16: Reconstructions for the non-ECG modalities at a light and a heavy corruption level: (a) PPG ( $24$ and $-6$ dB), (b) EMG ( $0$ and $-14$ dB), (c) EEG ( $5$ and $-5$ dB).

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DCRA: Diffusion-Conditioned Representation Alignment for Robust Time-Series Learning

Wenrui Xu, Anas Enanaa, Keshab K. Parhi

University of Minnesota, Twin Cities

Seizure Detection Representation Learning Electrocardiogram Foundation Models Diffusion Alignment Adversarial Corruption

Open paper AskPDF arXiv

Learning robust representations for time-series signals under noise and distribution shifts remains challenging, especially in clinical applications such as electroencephalogram (EEG) and electrocardiogram (ECG) analysis. We propose Diffusion-Conditioned Representation Alignment (DCRA), a training framework that repurposes the forward diffusion process as a structured corruption scheduler for representation learning. Different from conventional augmentation and consistency-based methods that rely on independently sampled perturbations, DCRA introduces a structured corruption trajectory via the diffusion forward process, which enables continuous and controlled representation evolution across noise levels. We introduce a feature-level consistency objective that aligns representations across noise levels while preserving class-discriminative structure. This mechanism promotes structure-preserving consistency, which enables smooth and semantically coherent feature trajectories in latent space. The proposed framework is encoder-agnostic and can be integrated with state space models and Transformer architectures. The seizure detection experiments on the CHB-MIT EEG dataset show that DCRA consistently improves performance under multiple noise conditions and achieves higher sensitivity at low false-positive rates. Analysis reveals that DCRA produces more balanced and structured representations compared to baseline and diffusion-only models. These findings highlight the benefit of combining structured corruption with representation alignment for robust time-series learning.

Abstract

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